17 research outputs found
An Empirical Study of the Manipulability of Single Transferable Voting
Voting is a simple mechanism to combine together the preferences of multiple
agents. Agents may try to manipulate the result of voting by mis-reporting
their preferences. One barrier that might exist to such manipulation is
computational complexity. In particular, it has been shown that it is NP-hard
to compute how to manipulate a number of different voting rules. However,
NP-hardness only bounds the worst-case complexity. Recent theoretical results
suggest that manipulation may often be easy in practice. In this paper, we
study empirically the manipulability of single transferable voting (STV) to
determine if computational complexity is really a barrier to manipulation. STV
was one of the first voting rules shown to be NP-hard. It also appears one of
the harder voting rules to manipulate. We sample a number of distributions of
votes including uniform and real world elections. In almost every election in
our experiments, it was easy to compute how a single agent could manipulate the
election or to prove that manipulation by a single agent was impossible.Comment: To appear in Proceedings of the 19th European Conference on
Artificial Intelligence (ECAI 2010
How Hard Is It to Control an Election by Breaking Ties?
We study the computational complexity of controlling the result of an
election by breaking ties strategically. This problem is equivalent to the
problem of deciding the winner of an election under parallel universes
tie-breaking. When the chair of the election is only asked to break ties to
choose between one of the co-winners, the problem is trivially easy. However,
in multi-round elections, we prove that it can be NP-hard for the chair to
compute how to break ties to ensure a given result. Additionally, we show that
the form of the tie-breaking function can increase the opportunities for
control. Indeed, we prove that it can be NP-hard to control an election by
breaking ties even with a two-stage voting rule.Comment: Revised and expanded version including longer proofs and additional
result
Detecting Possible Manipulators in Elections
Manipulation is a problem of fundamental importance in the context of voting
in which the voters exercise their votes strategically instead of voting
honestly to prevent selection of an alternative that is less preferred. The
Gibbard-Satterthwaite theorem shows that there is no strategy-proof voting rule
that simultaneously satisfies certain combinations of desirable properties.
Researchers have attempted to get around the impossibility results in several
ways such as domain restriction and computational hardness of manipulation.
However these approaches have been shown to have limitations. Since prevention
of manipulation seems to be elusive, an interesting research direction
therefore is detection of manipulation. Motivated by this, we initiate the
study of detection of possible manipulators in an election.
We formulate two pertinent computational problems - Coalitional Possible
Manipulators (CPM) and Coalitional Possible Manipulators given Winner (CPMW),
where a suspect group of voters is provided as input to compute whether they
can be a potential coalition of possible manipulators. In the absence of any
suspect group, we formulate two more computational problems namely Coalitional
Possible Manipulators Search (CPMS), and Coalitional Possible Manipulators
Search given Winner (CPMSW). We provide polynomial time algorithms for these
problems, for several popular voting rules. For a few other voting rules, we
show that these problems are in NP-complete. We observe that detecting
manipulation maybe easy even when manipulation is hard, as seen for example, in
the case of the Borda voting rule.Comment: Accepted in AAMAS 201
Eliminating the Weakest Link: Making Manipulation Intractable?
Successive elimination of candidates is often a route to making manipulation
intractable to compute. We prove that eliminating candidates does not
necessarily increase the computational complexity of manipulation. However, for
many voting rules used in practice, the computational complexity increases. For
example, it is already known that it is NP-hard to compute how a single voter
can manipulate the result of single transferable voting (the elimination
version of plurality voting). We show here that it is NP-hard to compute how a
single voter can manipulate the result of the elimination version of veto
voting, of the closely related Coombs' rule, and of the elimination versions of
a general class of scoring rules.Comment: To appear in Proceedings of Twenty-Sixth Conference on Artificial
Intelligence (AAAI-12
A Smooth Transition from Powerlessness to Absolute Power
We study the phase transition of the coalitional manipulation problem for
generalized scoring rules. Previously it has been shown that, under some
conditions on the distribution of votes, if the number of manipulators is
, where is the number of voters, then the probability that a
random profile is manipulable by the coalition goes to zero as the number of
voters goes to infinity, whereas if the number of manipulators is
, then the probability that a random profile is manipulable
goes to one. Here we consider the critical window, where a coalition has size
, and we show that as goes from zero to infinity, the limiting
probability that a random profile is manipulable goes from zero to one in a
smooth fashion, i.e., there is a smooth phase transition between the two
regimes. This result analytically validates recent empirical results, and
suggests that deciding the coalitional manipulation problem may be of limited
computational hardness in practice.Comment: 22 pages; v2 contains minor changes and corrections; v3 contains
minor changes after comments of reviewer